Turbulence: new research ends decade-long physics debate

Turbulence. The word often conjures feelings of bouncing back and forth in an airplane seat. You tighten your grip on the armrests, and the intercom crackles, “Ladies and gentleman, the captain has turned on the fasten seatbelt sign.”

But here on the ground, turbulence is everywhere. It’s what causes smoke to curl as it rises from a chimney, and mixes milk in your coffee as you stir. It also comes off your lips when you say things like ‘foxy’ or ‘pirate ship’.

Despite its ubiquity, scientists have struggled to predict and understand turbulence since the day we discovered it. Recent experiments have even disputed the most basic principles we thought we knew, threatening the accuracy of tools that many engineers need to model and simulate it.

However, new research in the Journal of Fluid Dynamics from the University of Toronto Institute for Aerospace Studies (UTIAS) has provided conclusive evidence that reinforces these basic principles and ends a decade-long debate in the field.

Published by PhD student Jason Hearst and Professor Philippe Lavoie (UTIAS), the study ensures the precision of our modern understanding of turbulence.

Writer RJ Taylor spoke to Lavoie to better understand why his research matters to engineering as we know it.

Turbulence refers to more than just airplanes and stock markets — can you explain what it is?

Turbulence can happen during any fast flow of liquids or gases. When the flow velocity increases past a certain value, among other things, it can become unstable and break down to a more chaotic state. (We refer to this as reaching a certain critical Reynolds number, a measure of the importance of inertial forces versus viscosity in a fluid flow). This results in a series of rapid fluctuations in velocity that we call turbulence. It can often appear as swirling patterns called eddies.

One way to understand turbulence is by looking in our kitchen sink. When you turn the tap on slowly, there is a smooth, steady stream of water. If you open the tap all the way, this smooth stream breaks down and the water can spray everywhere. Affected by speed, friction and other aspects, the flow reaches a high enough Reynolds number that viscosity can no longer dampen the instabilities. It becomes turbulent.

Another example can be found by looking at smoke rising off an incense stick. When the smoke first leaves the tip, it usually rises in a straight uninterrupted line. But as the jet of hot smoke rises, it becomes unstable and it starts to break down. That’s when you see the wisps and swirls of smoke, and that’s turbulence.

Why is it important for engineers to understand turbulence?

Turbulence affects engineers in almost every field, even weather prediction. This is because most industrial fluid flows are turbulent, as we often try to move a lot of liquids or gases very quickly. Just look at oil in a pipeline, air in a combustion engine, drainage under a city street and more.

Although there are no close-formed solutions to mathematically describe it, there are some fundamental concepts that help us to understand key aspects. These are incorporated in models that we use to build computer simulation tools.

It’s these tools that engineers use to design and test any number of systems across many industries. In order for their simulations to be accurate, we must understand the basic principles of turbulence.

Could you explain the debate your research addressed?

About 10 years ago, researchers started examining something called fractal turbulence. They would pass a fluid flow through a fractal object, such as a grid, so that it forces the turbulence at different scales. They can then see how it’s affected.

The results of these experiments did not behave as we would have expected, and thus seemed to suggest that our previous understanding of turbulence was wrong on some very fundamental points. It questioned some of the basic principles of turbulence theory. 

And this brought significant debate over the past decade in your field. What did your results show?

To examine this debate, my PhD student, Jason Hearst, and I used a wind tunnel to test a new type of fractal grid that we designed. Our grid allowed us look at the problem in a different way than anyone had before.

Through this experiment, we were able to reconcile both regular and fractal grid turbulence data. We conclusively showed that fractal turbulence was behaving the same way as classical turbulence, which has not been shown before.

Although fractal turbulence has some different features, it’s not fundamentally different. This evidence settled a long debate, as it demonstrated that our understanding of turbulence does not need to be fundamentally altered.

What impact does this have for engineers?

Engineers rely on accurate computer simulation tools to design many processes and systems. If those simulation tools are incorrect, it has significant impact on the resulting efficiency of these fluidic systems.

When you’re designing a heat exchanger, for example, the rate at which heat will be transferred depends on the turbulence in the flow field. So you need to be able to model that turbulence properly.

Also, what would happen if we did not have precise simulations for a new airplane wing design? The plane might not ever get off the ground.

Why hasn’t this debate been settled earlier?

It’s like the Indian parable about the blind men and the elephant. Each one only touches one part of the elephant, and given the limited information that each obtains, they all think they’re touching something very different.

It was basically a case of that. We thought we were looking at a different beast, because we weren’t looking at the whole picture. It just turns out we were just putting our finger on a different spot.

(Parts of this interview have been condensed and edited.)

RJ Taylor is a writer with the Faculty of Applied Science & Engineering